ERAChas - A Simple Coolant Math Problem

[patrickt]

Chas, RodKnock's engine is now two years old and he knows he needs to change the coolant but doesn't want to hassle with burping the notorious FE air pocket that always develops, flushing the the heater core, etc. so he came up with a wonderful "simple" method for changing the coolant the "EZ way." Rod is going to simply open the petcock at the bottom of the radiator and drain one gallon of old coolant in to a catch basin while simultaneously filling his surge tank with one gallon of new coolant so that it is always full and no air gets in to the system. Just one gallon, mind you; no more. He will then take the car for a ride to thoroughly circulate the coolant, let the car cool, then drain another gallon of old coolant out while simultaneously replacing it with a new gallon. But Rod is smart, he realizes that his system holds four gallons and that while the first drain and fill replaced 25% of that old coolant with new coolant, the second drain actually had one quarter of a gallon of new coolant in it, so he was really only replacing three quarters of a gallon of old coolant. After two "drain and fills" he now has a system with two and one quarter gallons old coolant and one and three quarters new coolant. Rod says he will be happy if he can replace 90% of his old coolant with new coolant. How many times will he have to repeat his "drain one gallon while adding one gallon and then drive" task in order to achieve his goal of a 90% coolant change? Show your work for full credit.

[mr0077]

Four gallons = 512 ounces of liquid. If he wants to change out at least 90% of the old fluid, he can allow 10%, or 51.2 oz of old fluid left in the system. Each time he changes 1/4 of the fluid he leaves 3/4 (75% or 0.75) of whatever is in it. If he did this routine 8 times, he would have 512 x 0.75^8 of old fluid. 0.75^8 = 0.1001, roughly 10%, so 512 x 0.75^8 = 51.2578 oz, slightly more than 10% old fluid. Therefore he has to do this change 9 times to have 10% or less of the old fluid (he would have 7.51% old fluid and 92.49% fresh fluid, or 473.5566 oz of fresh fluid and 38.4434 oz of old fluid.

Why did I just do that?

[Bob In Ct]

He's walking halfway to the wall. BTW - the answer is 8 times.

Bob

[patrickt]

Originally Posted by mr0077

Each time he changes 1/4 of the fluid he leaves 3/4 (75% or 0.75) of whatever is in it.

The ratio of good to bad coolant changes on each iteration. It is not a 1/4 to 3/4 constant.

[RodKnock]

The problem is specious. The fluid in the coolant system was changed March 2009 at the same time a coolant recovery tank was added.

Heater core? Puh-leeze. I didn't mark PS, AC, PW, PB, PDL and convertible top on the option sheet either.

And no. I don't have cupholders either.

[patrickt]

Originally Posted by RodKnock

The problem is specious.

True, but only because Chas will not be able to figure it out.

[RodKnock]

BTW, no traditional coolant either. A little bottle of Water Wetter and Pencool and the rest is distilled water.

[ERA Chas]

Originally Posted by patrickt

True, but only because Chas will not be able to figure it out.

Nooooooo...because Chas will not be stupid enough to dignify child games with a reply as poor Ken realized he had done.

Pat-did you get bounced off the Harry Potter Forum? Ran out of broken parts to flood us with macro digital full-color close ups? Slow night over on FE?

Well Rod, our precocious child is at it again. This is why he has 11,059 posts (ELEVEN THOUSAND FIFTY-NINE). I wish Keith, Barry, George, Clayton, Acton, Tom, Kincade and Mike had 11,000-(they don't have that many combined). We would all learn far more about our cars and motors and not Readers Digest popcorn games.

What's next to entertain we children Mr. Wizard-find the rabbit in the maze pictures?

A valuable help to any hands-on guys is this tip: block drains. Put brass petcocks in place of the block drain plugs, attach tubing to reach into your drain pan. When changing, drain from the lower rad hose, and both petcocks. You get a complete purge that way and refill through the temp sensor boss on the intake.

Now that's something people can use.

[patrickt]

Originally Posted by ERA Chas

Nooooooo...because Chas will not be stupid enough to dignify child games with a reply as poor Ken realized he had done.

Actually he did a very nice job. When I ran the numbers, 8 changes would get you an 89.99% coolant change... but, that ain't 90%, so he is technically correct.

Originally Posted by ERA Chas

Put brass petcocks in place of the block drain plugs, attach tubing to reach into your drain pan. When changing, drain from the lower rad hose, and both petcocks. You get a complete purge that way and refill through the temp sensor boss on the intake.

Uhhh, I would rather just change a gallon out after eight drives.

[blykins]

Don't make me break out the differential calculus on you Patrick.

[patrickt]

It's really an interesting question. When you open the petcock on, say, an ERA, it is on the lower driver's side of the radiator. The upper radiator hose goes to the top driver's side of the radiator, lower radiator to the bottom passenger side. If there are three or four holes drilled in the thermostat, will the fluid coming out the petcock be equal amounts from both the radiator and the block?

[ERA Chas]

Originally Posted by patrickt

Uhhh, I would rather just change a gallon out after eight drives.

For a guy that loves to brag about his he-man solid lifter noise, you're some pu$$y when it comes to doing actual WORK.

Surprised a cam that small can actually make noise. Get a free matching dress with that cam?

[patrickt]

Originally Posted by ERA Chas

Surprised a cam that small can actually make noise. Get a free matching dress with that cam?

No, but I got a POS dampNer.

Blykins, will the coolant level in the block and the coolant level in the radiator decline at an equal rate when the petcock is opened? I never took a fluid dynamics class....

[RodKnock]

Originally Posted by ERA Chas

Surprised a cam that small can actually make noise. Get a free matching dress with that cam?

Now that's funny.

But it's the "K" cam. Or was it the "R" cam? "B" cam? Eh doesn't matter.

To be honest with you, if I were doing it, then I would have to "wear the dress" and take 8 drives.

[patrickt]

Originally Posted by RodKnock

Now that's funny.

But it's the "K" cam. Or was it the "R" cam? "B" cam? Eh doesn't matter.

To be honest with you, if I were doing it, then I would have to wear the dress and take 8 drives.

It's the "K" cam, thank you very much. DCDoug has the "B" cam.

[elmariachi]

Finally, proof of the infinite monkey theorem.

[patrickt]

Ahh, the road to Hell... All I try to do is help RodKnock change his coolant and what does it get me.

[ERA Chas]

Originally Posted by elmariachi

Finally, proof of the infinite monkey theorem.

A perfect explanation of our 'clever' counselor...

[patrickt]

Originally Posted by ERA Chas

A perfect explanation of our 'clever' counselor...

Isn't it past your bed time?

[ERA Chas]

Originally Posted by patrickt

Isn't it past your bed time?

NAAAAhhhh-I enjoyed watching the Mets beat the crap out of your team while I beat the crap out of you here